The chemical meaning of topological indices

Saudi Pharmaceutical Journal, 2016

A massive of early drug tests implies that there exist strong inner relationships between the bio-medical and pharmacology characteristics of drugs and their molecular structures. The forgotten topological index was defined to be used in the analysis of drug molecular structures, which is quite helpful for pharmaceutical and medical scientists to grasp the biological and chemical characteristics of new drugs. Such tricks are popularly employed in developing countries where enough money is lacked to afford the relevant chemical reagents and equipment. In our article, by means of drug molecular structure analysis and edge dividing technology, we present the forgotten topological index of several widely used chemical structures which often appear in drug molecular graphs.

Acta Chimica Slovenica

From the G(a,b,c) matrix at least 20 groups of topological indices can be derived. Each of these groups contains an infinite number of possible indices. Some of these indices correlate by abs(r) max > 0.99, and a number of them by abs(r) max > 0.9 with particular tested 29 resp. 31 physicochemical properties of alkanes. Therefore, their use in QSPR/QSAR models is recommended. The indices of these groups are not useful to predict the physicochemical properties: dc, Zc, A, Cohesive Energy Density, and Solubility Parameter. the non-diagonal matrix elements; original indices raised to several exponents, e.g.

Journal of Structural Chemistry, 1990

Journal of Mathematics

In quantitative structure-property and structure-activity relationships studies, several graph invariants, namely, topological indices have been defined and studied due to their numerous applications in computer networks, biotechnology, and nanochemistry. Topological indices are numeric parameters that describe the biological, physical, and chemical properties depending on the structure and topology of different chemical compounds. In this article, we inaugurated some degree-based novel indices, namely, geometric-harmonic GHI , harmonic-geometric HGI , neighborhood harmonic-geometric NHGI , and neighborhood geometric-harmonic NGHI indices and verified their chemical applicability. Furthermore, an attempt is made to calculate analytical closed formulas for different variants of silicon carbides and analyze the obtained results graphically.

Symmetry

A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randi c ´ , atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randi c ´ index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.

Journal of Chemistry, 2020

Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.

Discrete & Continuous Dynamical Systems - S

Topological indices defined on molecular structures can help researchers better understand the physical features, chemical reactivity, and biological activity. Thus, the study of the topological indices on chemical structure of chemical materials and drugs can make up for lack of chemical experiments and can provide a theoretical basis for the manufacturing of drugs and chemical materials. In this paper, we focus on the family of smart polymer which is widely used in anticancer drugs manufacturing. In chemical graph theory, a topological index is a numerical representation of a chemical structure which correlates certain physico-chemical characteristics of underlying chemical compounds e.g., boiling point and melting point. More preciously, we focus on the family of smart polymer which is widely used in anticancer drugs manufacturing, and computed exact results for degree based topological indices.

QSAR & …, 2004

The primary goal of a quantitative structure-property relationship (QSPR) is to identify a set of structurally based numerical descriptors that can be mathematically linked to a property of interest. Recently, we proposed some new topological indices (Sh indices) based on the distance sum and connectivity of a molecular graph that derived directly from two-dimensional molecular topology for use in QSAR/QSPR studies. In this study, the ability of these indices to predict the liquid densities (r) of a large and diverse set of organic liquid compounds (521 compounds) has been examined. Ten different Sh indices were calculated for each molecule. Both linear and non-linear modeling methods were implemented using principal component regression (PCR) and principal component-artificial neural network (PC-ANN) with back-propagation learning algorithm, respectively. Correlation ranking procedure was used to rank the principal components and entered them into the models. PCR analysis of the data showed that the proposed Sh indices could explain about 91.82% of variations in the density data, while the variations explained by the ANN modeling were more than 97.93%. The predictive ability of the models was evaluated using external test set molecules and root mean square errors of prediction of 0.0308 g ml À1 and 0.0248 g ml À1 were obtained for liquid densities of external compounds by linear and non-linear models, respectively.

Journal of Chemical Information and Modeling, 2007

The sequence of all paths p i of lengths i) 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Σ i p i 2 , and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q) Σ i p i 2 /(µ+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Σ i p i 1/2 , and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S) Σ i p i 1/2 /(µ+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D) Σ i {p i 1/2 /[i(µ+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A) Σ i {p i /[i(µ + 1)]}; and (v) the last TI with two square roots: Path-count index: P) Σ i {p i 1/2 / [i 1/2 (µ + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property. † Dedicated to Professor Nenad Trinajstić on the occasion of his 70th birthday.

Journal of Chemical Information and Computer Sciences, 1997

A novel, distance-cum-adjacency topological descriptor, termed as eccentric connectiVity index, has been conceptualized, and its discriminating power has been investigated with regard to physical/biological properties of molecules. Correlation coefficients ranging from 95% to 99% were obtained using eccentric connectivity index in various datasets with regard to physical properties of diverse nature. These correlations were far superior to those correspondingly derived from the Wiener index. For structure-activity studies, a dataset, comprised of 94 substituted piperidinyl methyl ester and methylene methyl ester analogs as analgesic agents, was selected. Values of the eccentric connectivity index, the Wiener index, and Randić's molecular connectivity index were calculated, and active ranges were identified. Good correlations between topological descriptors and analgesic activity of these analogs were obtained. Eccentric connectivity index exhibited highest predictibility of the order of 86%. High discriminating power as revealed by excellent correlations obtained from structure-property and structure-activity studies offers an eccentric connectivity index of vast potential in QSPR/QSAR.